The multivariate Hermite method for counting real and complex solutions to polynomial systems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912831181422592 |
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| author | Oleksiyuk, Volodymyr |
| author_facet | Oleksiyuk, Volodymyr |
| contents | This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final section includes an implementation in Macaulay2, a free and open-source computer algebra system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The multivariate Hermite method for counting real and complex solutions to polynomial systems Oleksiyuk, Volodymyr Algebraic Geometry 14Q30 (primary), 14P20, 13P10 (secondary) This note presents the multivariate Hermite criterion: a practical and powerful algorithm for determining the number of distinct real and complex roots of a zero-dimensional system of polynomials in any finite number of variables. The final section includes an implementation in Macaulay2, a free and open-source computer algebra system. |
| title | The multivariate Hermite method for counting real and complex solutions to polynomial systems |
| topic | Algebraic Geometry 14Q30 (primary), 14P20, 13P10 (secondary) |
| url | https://arxiv.org/abs/2510.23897 |